p = 1/2

## Build the grid that represents the possible outcomes at each point in time to plot:
##
reductions = c(-1, +1) ## how much does our price change

n_steps = 3

seg_x0 = c()
seg_y0 = c()
seg_x1 = c()
seg_y1 = c()

current_nodes = c(0) ## the initial price

for( yi in 1:n_steps ){
    new_current_nodes = c()

    for( pti in 1:length(current_nodes) ){
        xx = yi-1
        yy = current_nodes[pti]

        ## Create a segment from (xx, yy) -> (xx+1, yy + reduction):
        ##
        for( rai in 1:length(reductions) ){
            xxp = xx+1
            yyp = yy + reductions[rai]

            new_current_nodes = c(new_current_nodes, yyp)

            seg_x0 = c(seg_x0, xx)
            seg_y0 = c(seg_y0, yy)
            seg_x1 = c(seg_x1, xxp)
            seg_y1 = c(seg_y1, yyp)
        }
    }

    current_nodes = new_current_nodes
}
##print(cbind(seg_x0, seg_y0, seg_x1, seg_y1))

##postscript('../../WriteUp/Graphics/Chapter12/chap_12_ex_9_outcomes.eps', onefile=FALSE, horizontal=FALSE)
plot(NULL, xlim=c(0, max(c(seg_x0, seg_x1))+0.5), ylim=c(min(c(seg_y0, seg_y1)), max(c(seg_y0, seg_y1))), xlab='toss number', ylab='N_heads - N_tails', xaxt='n')
segments(seg_x0, seg_y0, seg_x1, seg_y1)
axis(1, at=0:4, labels=c('0','1','2','3','4'))
final_state = sort(unique(seg_y1[seg_x1==n_steps]), decreasing=T)

points(rep(4, length(final_state)), final_state, type='p', pch=19)
text(rep(n_steps, length(final_state))+0.1, final_state, labels=c(27, 27, 0, 0))

text(0.25, 0, labels='V_1')
text(1.25, -1, labels='V_2')
text(1.25, 1, labels='V_3')
text(2.25, -2, labels='V_4')
text(2.25, 0, labels='V_5')
text(2.25, 2, labels='V_6')

points(rep(2, 3), c(-2, 0, 2), type='p', pch=19)
text(rep(2, 3), c(-1.75, 0.25, 2.25), labels=c(0, 9, 27))

points(rep(1, 2), c(-1, 1), type='p', pch=19)
text(rep(1, 2), c(-0.75, 1.25), labels=c(3, 15))

points(0, 0, type='p', pch=19)
text(0, 0.25, labels=c(7))
##dev.off()

print('In three coin flips N_heads - N_tails= ')
print(round(final_state, 2))